Since the vehicle is a 2001 or 19 years old… and One side was very hot and the other not - I don’t believe that it is air in the system. The heat from the passenger side - is that the brakes were staying ON… the fluid than gets hot and starts boiling; which becomes a VAPOR in the lines - and your brakes become soft and spongy and do not work… Brake fluid absorbs water (moisture) from the air and becomes ‘diluted’ and the boiling temp becomes lowered quite a bit. You should probably have the brake fluid changed out.
However - WHY did the one side become so Hot and start interfering with your brakes? This could very well be caused by the age of your brake hose lines. The brake HOSE going to the caliper is subject to deterioration - and can get to the point where when you release the brakes (take your foot of the pedal) - the brake hose COLLAPSES or PINCHES - and the brake fluid is NOT released from the Caliper. This causes the brake to stay ON and it becomes very HOT - which causes the fluid to boil; which causes you to lose your brakes. When you apply the brakes - the hose is FILLED with fluid (pressurized) and moves the caliper - and the brake hose is EXPANDED; and when you release the brakes - the deteriorated hose COLLAPSES just a bit and causes a pinch - and fluid is not released - and you get the situation you are describing. I suggest you replace both caliper brake hoses; and any brake HOSE (not steel tubing) - in the same vicinity - on both sides of your brakes; get the fluid flushed… and you will probably be fine after that. I apologize if this is not it - I did not read all the previous comments - but this specific incident did happen to me - on a 1992 truck that I own… If this does not fix it - you should definitely take it to a good mechanic. But a simple deterioration of the brake hose can cause the pedal to sink to the floor - because the hose pinches when the pedal is released; the brake fluid becomes hot and starts to boil - and now you have VAPOR and not fluid in your brake line. And Vapor compresses; while fluid does not! And when it cools - it becomes a fluid again…